Matt Swartz on home field advantage

Baseball Prospectus's Matt Swartz has completed a nice five-part series on home-field advantage (HFA) in major league baseball. I've always thought HFA was one of the biggest unresolved issues in sabermetrics. So does Swartz, and he said it better than I could:

"[HFA] should surprise us as analysts more than it does. Nearly every study of psychology with respect to baseball has come up revealing either small effects or no effect. We all know that players are human, but the numbers do not seem to indicate many obvious psychological aspects. Hundreds of researchers have tried to discover clutch hitting, but few have found any evidence of its being a repeatable skill. ... We have attempted all kinds of ways to splice the data to reveal a large psychological effect within baseball to show that baseball players don’t behave like statistical models, and there seems to be little evidence of any strong, detectable effects, even if we know they exist and occasionally can discover smaller ones. ...

"However, home-field advantage is perhaps the most obvious area where we see something resembling a psychological effect, or at least an effect that is not captured by our typical models of baseball players and ballgames. It is clear that something about being the home team trumps talent in a way that is mathematically equivalent to benching an average player on the road team."

Swartz proceeds to look at various aspects of HFA. Many of the findings are unremarkable, but there are a couple that are kind of interesting.

First, let me quickly summarize the other stuff that Matt found in each of his five parts.

Part 1: HFA has been very steady over the decades, at around 40 points (.540 to .460). It shows up in almost every statistical category for hitters and pitchers, except those related to errors.

Part 2: There doesn't seem to be a team-specific HFA, except for the Rockies, whose HFA is an outlier and much higher than most.

Part 3: There appears to be a "familiarity" effect. HFA is highest for interleague games, next highest for games between teams in different divisions, and lowest for intradivisional games (where presumably the teams face each other most often). Also, the farther apart the teams, the higher the HFA.

Part 4: The second-last game of a series seems to have a larger HFA than any other game. This apparently only holds for teams who are geographically close together. Lots of other breakdowns show no significant effect.

Part 5: Individual players do appear to show stable HFAs from year to year, suggesting that they can be more or less suited to their home park.

Most of this is roughly in line with what we knew already. But here's the thing I found most interesting: a lot more of HFA comes in the first three innings than in the rest. Here's Swartz's chart; for each inning, the percentages are the difference in runs scored for the home team vs. the visiting team:

1 16.2%
2 9.3%
3 10.1%
4 6.0%
5 7.8%
6 8.1%
7 8.7%
8 6.5%

The overall difference appears to be about 8%. By Pythagoras, if a team scores 8% more runs than their opponents, they'll win a little over 16% more games, which works out to about a .540 winning percentage, exactly as observed (.540 divided by .460 equals 1.17). But the first inning number is huge! If the home team outscored the visiting team by 16.2% overall, its winning percentage would be .575 (Pythagoras with exponent 2).

What could cause this? It could just be that the first inning is higher-scoring overall, and the difference isn't linear. But the difference is still huge. Could this be a real finding, that HFA diminishes later in the game? If it's a question of familiarity, that might make sense, except that why would the visiting team be less familiar with the park the first inning of Game 3 as opposed to the eighth inning of Game 2?

Still, this is something I haven't seen before, and I wonder if you'd find the same thing if you looked at other sports.

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One thing that might be good is to break down HFA into its component parts. The articles show us the HFA appears in almost every statistical category, but they overlap. For instance, the home team strikes out less and walks more. This indicates that the visiting pitchers are throwing fewer strikes and more balls. Is that enough to be the entire effect? That is, if the road pitchers are getting behind in the count, the batters will do better, even if batting skill is completely unaffected by HFA. On 2-0, the batters will be seeing juicier pitches, and that alone could account for their extra doubles, triples, and home runs.

Does it? What you'd want to do to find out, is to compare batting lines based on count (and controlling for pitcher, if you really wanted to be thorough). As it stands now, we still don't really know what HFA comes from, whether it's evenly balanced between batter and pitcher, or what.

The home team scores, on average, about 0.4 runs per game more than the visiting team. Using Swartz's numbers and assuming 40 PA per game per team, the home team gets about 0.4 fewer strikeouts and 0.25 fewer walks. That adds up to about .18 runs. That's half the entire effect. Is it possible that just the different (favorable) counts account for the home team's remaining .22 run advantage? Seems possible to me.

Or, looking at it another way: a study I did a few years ago (.pdf, page 4) came up with the figure that turning a ball into a strike is worth about .14 runs. That's a three pitch per game difference between the two teams. Would a three pitch difference (three extra strikes and three fewer balls) be consistent with 0.4 extra strikeouts and 0.25 fewer walks? I don't know, but you could try looking at it that way.

If you went about it that way, you might wind up with a breakdown of HFA something like:

30% pitchers throwing more strikes
15% batters putting the ball in play more often
10% batters hitting a different LD/GB/FB mix
20% higher BABIP on a given type of ball in play
15% more HRs

I'm making these numbers up, of course. And for some of this stuff, you wouldn't be able to tell if it was the pitcher or the hitter; for instance, fewer strikes might just mean that the batter makes contact better, as opposed to the pitcher improving. And for a higher BABIP (which Swartz found), is it the hitters doing better, or the defense doing worse? We don't know. But still, a breakdown like that would be a start.

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Another thing I'd like to see is just raw performance data. Do pitchers throw harder at home than on the road? Do their pitches have more break or movement, all else being equal? That might be hard to study, because all else is never equal, and Pitch F/X recorders might be different at different parks. Although, if the Braves' pitchers show 2 MPH more than their opponents at home, but 1 MPH less on the road ... that does indeed tell you something, although the caliber of the opposition might not even out in your two samples.

My guess is that you'd find that HFA goes right down to the most base level imaginable: the home team would have higher bat speeds and pitch velocities. Their players would run faster at home, and they'd have faster reaction times. I suspect that HFA is something universal, and both psychological and physiological. I'd bet that within a few years, evolutionary psychologists will be studying this stuff and have some theories about how we evolved to be physically more competent in familiar surroundings.

But I'm just guessing.